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Options Theory: Options Greek Delta Measures Probability

December 27, 2021

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Today’s video introduces the three definitions of the options greek delta, with a focus on its probability measuring.


The Delta Trio:

Delta reflects PROBABILITY

1A) Delta measures the probability of an option expiring ITM.

                A) Buy a call with a 0.60 delta. There is a 60% chance that call will be ITM at expiration.

1B) 1 – delta measures the probability of an option expiring OTM.

                A) Sell a naked put with a 0.10 delta. There is a (1 – 0.10 = 0.90) 90% chance that put will expire OTM at expiration.

Delta as probability for these options strategies:

1) Long call/long put: Generally, we buy ITM, higher delta, higher odds bet. Less of a chance I lose all my money.

2)Naked Put/Bull Put: Generally, we sell OTM, low delta puts. Higher odds bet. If I sell 0.20 delta puts or less, I have an 80%+ probability of profit.

3) Bull Call spread: Generally, we don’t have a delta as probability rule on this. Because we’re more focused on Delta as a DIRECTONAL EXPOSURE.

                i. Buy 50 delta call, sell way OTM 25 delta call.

                ii. Create a rule that reflects probability of profit for a bull call spread. Buy lower strike call, usually ATM or slightly ITM. Sell an OTM call against it that has a delta between 0.30 to 0.20.

4) Covered Call: Buy 100 shares of stock, sell OTM call option (delta 0.40 and 0.30).

                i. There’s a 60% to 70% probability the call option will expire worthless.

We have delta guidelines when SELLING OPTIONS because we’re focusing on the PROBABILITY OF PROFIT aspect of Delta.

Sell 10 delta naked put, that’s like being long 10 shares of stock. You don’t have that much directional exposure! Delta tells me I have a 90% Probability of Profit.


2) Delta tells you how much money you make if the stock rises $1.00

                A) Buy call with a 0.60 delta, I make 60 cents per share per $1 move in the stock.

                B) Buy call with a 0.90 delta, I make 90 cents per share per $1 move in the stock.

                C) The higher the delta, the more sensitive your position to stock price movement.

Delta as Share Equivalency

3) 1 Delta = 1 share of stock

A) Buy 0.75 delta call = Owning 75 shares of stock.

B) AAPL options position, delta 325. It’s like I’m long 325 shares of stock.

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